I wrote this piece a few months ago on ecosystems and have been wondering what to do with it. If you read it, consider this: the world is an ecosystem and global warming is a non-linear process. Everybody talks about it, and what we do or don't do about it. Well here's a twopenniworth from a concerned grape grower.

For a long time people thought about nature as being a system which had a natural balance. Nature was some sort of divine management system conducted by... depending on your philosophy... an outside intelligence or by the sheer mathematics that underlie Darwinian thought.

In the last few decades a clearer understanding has emerged. It may be clearer, but it is far more difficult to grasp, so this progress has largely been ignored by those outside the scientific community.

Now global warming, climate change, sustainability, a whole raft of major issues, are entering the public arena and the ability to properly understand the system is suddenly becoming very important. So here goes: and by the way, if you can't understand any of this, dont worry, that just means you are probably getting it right. Reality can be pretty strange at times.

This is about a very difficult area of mathematics. For a while it didn't have a name (but was often viewed as a part of a branch of mathematics called topology). Then as people started to seriously explore it, it acquired a name: chaos theory. As understanding grew it became clear that the word chaos was a very bad description of what was being discovered; this was something that was anything but chaotic. Today it is known as complexity theory.

Who cares about maths? Only mathematicians, and we aren't going to go near the maths of all this, which, believe me, is seriously scary stuff. The point is that all of this is not some random process nobody understands. It is governed absolutely by mathematics and maths doesn't require you to understand it for it to work: four pregnant rabbits each giving birth to three rabbits results in 12 baby rabbits and did so long before anybody knew how to multiply.

So what does drive ecosystems? (Or climate, for that matter since both are governed by the same maths principles.)

Ecosystems are non-linear systems. A system is usually non-linear when more than one factor mutually affects other factors. The mutual bit is the important part as it results in a feedback loop. For example: wolves eat deer. The more wolves, the more deer get eaten, so the less deer there are to breed, so the fewer deer there are to eat, so the less wolves have to eat, so the fewer wolves, so less deer get eaten. You get the idea: any change to one side changes the other side, which in turn changes the first side, which again changes the second and so on for ever. It looks like a cycle, but it isn't. Ever.

Non-linear systems turn up all over the natural world. For a very long time it was assumed that this was just normal mathematics, but nobody could ever figure out equations that could solve it. Insights into the maths have happened over the last 100 years but they were just glimpses of stuff so horrifically anarchic that the term chaos was eventually coined to describe their behaviour. It took big computers to pick the stuff apart enough to understand there is nothing chaotic at all: rather an incredible world of structure of literally infinite detail. Run non-linear models through computers and you see wonderful images of great beauty, images that often look uncannily like natural living things.

All well and good, but what does this tell us about the world about us. More important what advice can it impart?

There are some very important messages:

1.Non-linear systems are inherently not predictable.

That doesn't mean they are hard to predict, or we don't know how to predict them, it means it is an intrinsic property of them that they can never be predicted. You could come back in a thousand years to a hugely advanced society (hopefully) and just as two and two will still equal four, non-linear systems will still be not be predictable.

2.Non-linear systems never return to the same point twice.

Again, this isn't just that there are so many points they are unlikely to go back: they cannot go back. That is an unbreakable law of non-linearity. This means nature cannot be cyclical: there cannot ever be a cycle, simply a return to a similar but not identical state. The most important factor here is that if a system is at a point very close to a previous point (let's call it A) and the last time the system progressed from there to a point B that is no indicator that this time around it will move to a point close to point B. It can and probably will do something completely different.

3.Non-linear systems normally move around an attractor.

This one is tougher. What is an attractor? Answer, it is the thing the system moves around. No more than that. It isnt actually a thing, it has no existence of itself, it is a point of mathematical harmony which these staggeringly difficult equations seem to enjoy hovering around, just as bees like certain flowers. This a critical difference between something chaotic; which would be non-predictable and have no pattern, and something complex; which is non-predictable, but has a very profound and exact pattern. This an interesting dilemma: here is something that is anything but random, that is, in fact, very highly ordered, but is absolutely unpredictable. Weird stuff.

4.Non-linear systems can be knocked off an attractor with radical consequences.

Sometimes one can make quite a large change to a non-linear function, but it still continues to settle back around its attractor. On other occasions, the smallest interference can cause a system to leave its attractor. When this happens, if a system leaves its attractor the effects are both very dramatic and irreversible. They are, as we've mentioned before, also unknowable.

5.Just as the system is inherently unpredictable, one cannot predict which changes to a system will have radical results.

So there's no point in asking what actions are the dangerous ones: we don't know and we cannot know.

Here we have a problem. If we don't know and cannot know what actions are the dangerous ones, how on earth do we create a strategy for sustainability? Isnt this a charter for people to say that the maths proves that there is no point in taking action? Or, for that matter, no point in worrying about changes that affect the non-linear systems that drive almost all the aspects of the world about us. This is out of our hands and out of our sphere of knowledge.

These things are true, but that doesnt mean we can't build a sound strategy from the knowledge we do have.

Which brings us to throwing stones at a train.

You find out your child has been throwing stones at trains as they go past. You tell them it is dangerous to do that.

"But Tommy throws stones at trains"

"Tommy shouldn't; it's dangerous"

"But nothing's happened"

"But if you keep on doing it, something bad will happen"

"How many stones can I throw before its dangerous?"

"It doesn't work like that, just one stone could do it"

"How big do they have to be to be dangerous?"

"It doesn't work like that, a tiny one could do it"

"How do you know which is the dangerous one?"

"You can't"

"So how do you know it's dangerous, then?"

It can be hard to explain that without any ability to predict, while the future is unknowable, there is nevertheless an ever growing chance that one day one of those stones will hit a microscopic flaw in a windscreen, a slice of glass will go through the driver's eye, and in a terrible microsecond the system leaves its attractor, never to return.

So, a strategy:

You're not trying to go back.

You're not trying to keep things as they are.

You're not trying to keep a cycle going.

You're not trying to tell the future.

You are just trying not to throw stones at the trains as they go past.

After a lot of thought we have decided not to use Facebook or Twitter. We like longer conversations and for them to be personal not public. If we did it, it would be because it is a fashion and not because our heart is in it and that doesn’t feel right. So please email, or much better come and see us.